In [4]:
import kwant
import numpy as np
import scipy
from matplotlib import pyplot
import kwant.continuum
hamiltonian = "k_x**2 + k_y**2"
template = kwant.continuum.discretize(hamiltonian)
print(template)
energies = []
step=0.021
nsteps=350
fermid0=[]
fermid1=[]
current2=[]
current3=np.zeros((15,8))
mu0=2.51
vbias=0.1
mu1=mu0+vbias
temperature=0.15
for ie in range(nsteps):
energy = ie * step
energies.append(energy)
fd0=kwant.kpm.fermi_distribution(energy, mu0,temperature)
fd1=kwant.kpm.fermi_distribution(energy, mu1,temperature)
fermid0.append(fd0)
fermid1.append(fd1)
pyplot.figure()
pyplot.plot(energies, fermid0)
pyplot.plot(energies, fermid1)
pyplot.xlabel("energy [t]")
pyplot.ylabel("Fermi distribution")
pyplot.show()
z0=2
wdt0=2
t=1
a=1
lat = kwant.lattice.square(a,norbs=1)
# Definition of Up lead
sym_up_lead = kwant.TranslationalSymmetry((0, -a))
up_lead = kwant.Builder(sym_up_lead)
for j in range(20):
up_lead[lat(-23+j,0)] = 4 * t
if j > 0:
up_lead[lat(-23+j,0), lat(-23+j-1,0)] = -t
up_lead[lat(-23+j,1), lat(-23+j,0)] = -t
# Definition of Down lead
sym_down_lead = kwant.TranslationalSymmetry((0, a))
down_lead = kwant.Builder(sym_down_lead)
for j in range(20):
down_lead[lat(3+j,0)] = 4 * t
if j > 0:
down_lead[lat(3+j,0), lat(3+j-1,0)] = -t
down_lead[lat(3+j,1), lat(3+j,0)] = -t
# Construction of 2-parametric family of systems varying smoothness and the width of the third way
for nz in range(15):
z=z0+nz*12
# ДВА ПУТИ
def twoways(site):
(x, y) = site.pos
xl = max(abs(x) - 20, 0)
xs= max(abs(x) - 28, 0)
return (1.2*xl**z + 1.2*y**z < 30**z and xs**z + y**z > 14**z)
syst2 = kwant.Builder()
syst2.fill(template,twoways, (0, 20));
syst2.attach_lead(up_lead)
syst2.attach_lead(down_lead)
if nz==0:
kwant.plot(syst2)
syst2 = syst2.finalized()
data2 = []
for ie in range(nsteps):
energy = ie * step
# compute the scattering matrix at a given energy
smatrix2 = kwant.smatrix(syst2, energy)
# compute the transmission probability from lead 0 to
# lead 1
data2.append(smatrix2.transmission(1, 0))
prd0=np.multiply(data2,fermid0)
prd1=np.multiply(data2,fermid1)
Tcurrent01=scipy.integrate.simps(prd0, energies,even='avg')
Tcurrent10=scipy.integrate.simps(prd1, energies,even='avg')
Tcurrent=Tcurrent01-Tcurrent10
print(Tcurrent)
current2.append(Tcurrent)
for nw in range(8):
wdt=wdt0+nw*2
# ТРИ ПУТИ
def threeways(site):
(x, y) = site.pos
xl = max(abs(x) - 20, 0)
xs= max(abs(x) - 28, 0)
return (1.2*xl**z + 1.2*y**z < 30**z and xs**z + y**z > 14**z) or (abs(x)<wdt and abs(y)<25.5)
syst3 = kwant.Builder()
syst3.fill(template,threeways, (0, 10));
syst3.attach_lead(up_lead)
syst3.attach_lead(down_lead)
syst3 = syst3.finalized()
#kwant.plot(syst3)
data3 = []
for ie in range(nsteps):
energy = ie * step
# compute the scattering matrix at a given energy
smatrix3 = kwant.smatrix(syst3, energy)
# compute the transmission probability from lead 0 to
# lead 1
#energies.append(energy)
data3.append(smatrix3.transmission(1, 0))
prd0=np.multiply(data3,fermid0)
prd1=np.multiply(data3,fermid1)
Tcurrent01=scipy.integrate.simps(prd0, energies,even='avg')
Tcurrent10=scipy.integrate.simps(prd1, energies,even='avg')
Tcurrent=Tcurrent01-Tcurrent10
print(Tcurrent)
current3[nz,nw]=Tcurrent
pyplot.figure()
pyplot.plot(energies, data2,color = 'b')
pyplot.plot(energies, data3, color = 'g')
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
# Discrete coordinates: x y # Onsite element: (4+0j) # Hopping from (1, 0): (-1+0j) # Hopping from (0, 1): (-1+0j)
C:\Users\Planeswalker\anaconda3\lib\site-packages\sympy\__init__.py:672: SymPyDeprecationWarning: importing sympy.matrices.matrices with 'from sympy import *' has been deprecated since SymPy 1.6. Use import sympy.matrices.matrices instead. See https://github.com/sympy/sympy/issues/18245 for more info. self.Warn( C:\Users\Planeswalker\anaconda3\lib\site-packages\sympy\__init__.py:672: SymPyDeprecationWarning: importing sympy.matrices.matrices with 'from sympy import *' has been deprecated since SymPy 1.6. Use import sympy.matrices.matrices instead. See https://github.com/sympy/sympy/issues/18245 for more info. self.Warn(
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